Dimensions

• Positions: Goalkeeper, Defender, Midfielder, Forward
• Subroles: GK (Goalkeeper), CB (Center Back), FB (Full Back), CM (Center Middle), DMC (Defensive Middle Center), CAM (Center Attacking Middle), WAM (Wing Attacking Middle), FW (Forward)
• Leagues: Serie A, Premier League, La Liga, Bundesliga, Ligue 1, Primeira Liga
• Seasons: 2017, 2018, 2019, 2020

Players by Position

Players by League

Players by Position and League

Features

Goalkeepers

Defenders, Midfielders and Forwards

Algorithms

• Dimensionality Reduction: UMAP - Non-linear dimensionality reduction method, very effective for visualizing clusters or groups of data points and their relative proximities.

• Clustering: DBSCAN - Density-based clustering technique that separates dense regions in space from regions of lower density, expanding them recursively to find dense arbitrarily shaped clusters.

UMAP

The intuition behind UMAP is that it constructs a high dimensional graph representation of the data first, and then optimizes a low-dimensional graph to be as structurally similar as possible.

It relies on the manifold hypothesis or assumption, which holds that most real-world high-dimensional datasets lie close to a much lower-dimensional manifold.

In this way, it preserves the data’s global structure, meaning that both within cluster and between cluster distances are guaranteed. This represents an advantage against other non-linear techniques like t-SNE (it is also much faster to achieve convergence).

DBSCAN

The main idea behind DBSCAN is that clusters are dense regions in space separated by regions of lower density. The algorithm finds these dense areas and expands them recursively to find dense arbitrarily shaped clusters.

There are three key parameters to consider:

• minPts: minimum number of data points to define a cluster.
• eps: distance that specifies the neighbourhoods. Two points are neighbours if the distance between them is less than or equal to eps.
• distance metric: by default, it uses Euclidean distance, although other methods can also be used.

We will default the distance metric to the Euclidean, and we will tune minPts and eps to find the most representative clusters possible.

In order to determine the optimal value of eps, we will set a value for minPts and make use of the average distances of every point to its k nearest neighbors, where k will be minPts. These k distances are then plotted in ascending order, to get an elbow plot. The distance where a sharp change (elbow) in the curve can be seen is the theoretical optimal value for eps.

Analysis

The analysis of the roles in a football pitch will be divided by league and position. Firstly, we will analyze the leagues altogether to try to find general patterns and clusters. Secondly, we will perform the same analysis for each separate league and evaluate if there are significant differences among them.

The analysis conducted for each league and position will contain 5 sections:

• Dimensionality Reduction + Clustering: UMAP + DBSCAN application to the data in order to extract meaningful clusters.

• Cluster Distribution: analysis of how positions and subroles are distributed among each identified cluster.

• Cluster Evaluation: technical evaluation of within and between clusters’ performace using silhouette score. This value ranges from −1 to +1, where a high value indicates that the players are well matched to their own cluster and poorly matched to neighboring clusters.

• Cluster Interpretation: supervised learning using the clusters’ labels as the target variable to interpret which players’ characteristics describe each group and how do they interact with each other.

• Cluster Composition: tables of players by cluster to understand them and validate if they make sense.

We will exclude the goalkeepers from the analysis, since the nature of the role is completely different from the rest and the identification of subroles is not so relevant.

Clustering

• Cluster 1: outliers, intended as unique players whose characteristics distinguish them from the rest of the dataset (both in good and bad sense!). Some champions included here are Lionel Messi, Cristiano Ronaldo, Kevin De Bruyne and Aymeric Laporte.

• Cluster 2 mainly groups center-backs with high clearances and recoveries but no offensive participation.

• Cluster 3 is very heterogeneous and groups those players with a high offensive propensity, independent on the role. Indeed, only center-backs are excluded from this cluster.

• Cluster 4 includes center-backs together with some full-back and defensive midfielder. They have good passing skills but are still not involved in the build-up phase.

• Cluster 5 is the full-backs’ cluster. As we will see in almost every league, these players are the ones with the most similar characteristics between each other.

• Cluster 6 includes almost all the center forwards.

• Cluster 7 is formed by physical central defenders with a good scoring record, like Harry Maguire.

• Cluster 8 groups all those central defensive players who mainly focus on men mark, but still being very effective when they have to pass the ball or even dribble the opponent (examples are Presnel Kimpembe and Ruben Dias).

• Cluster 9 includes highly heterogeneous central midfielers.

• Cluster 10 is a sort of residual group. The only common characteristic of these players is that they score above the average for their roles.

Cluster Distribution

We will examine the clusters in greater detail by looking at their composition by position and subrole:

Cluster Evaluation

   cluster size ave.sil.width
2        2  171          0.82
3        3 1659          0.40
4        4  531          0.63
5        5 1072          0.53
6        6 1405          0.36
7        7 1043          0.63
8        8  282          0.69
9        9  417          0.59
10      10  458          0.65
11      11  175          0.86

Cluster Interpretation

Decision Tree Accuracy:  68.02%

Cluster Composition